If you asking from a planning/estimation perspective, then I'd say plan for at least a week to be safe. There really aren't many hard and fast rules when it comes to harvesting from bottle dregs - it's far less predictable than building a starter from a smack pack or vial.
One "rule" when bottle harvesting is to keep the SG of your wort lower than normal, like 1.030 instead of the common 1.040. It's said to be gentler on the yeast. Then to build up any more significant numbers you'll have to step up the starter with another dose of wort. On subsequent times it's OK to do the normal 1.040. There are other "rules" for the volumes to be used in subsequent steps, but I don't often remember those.
I don't have any experience with that beer, but I'll tell you once when I harvested Pacman from a bottle of Dead Guy, it took about 72 hours to even see an initial "bloom". Then because it was the multi-step starter, it was another 48 hours for the next step. Then I decanted before pitching, so another couple of days.